Question

# Find the amount that results from the given investment. $700 invested at 4\% compounded daily after a period of 4 years: After 4 years, the investement results in how much$?

Modeling data distributions
Find the amount that results from the given investment. $$\displaystyle\{700}$$ invested at $$\displaystyle{4}\%$$ compounded daily after a period of 4 years:
After 4 years, the investement results in how much \$?

2021-08-10

Step 1
Compound interest:
In compound interest, interest is added back to the principal sum so that interest is earned on that added during the next compounding period. That is, compound interest will give an interest on the interest. The interest payments will change in the time period in which the initial sum of money stays in the bank or with the barrower.
The general formula for compound interest is,
$$\displaystyle{A}={P}\cdot{\left({1}+\frac{{r}}{{n}}\right)}^{{{n}{t}}}$$
Where:
A is the future value of the investment loan including the loan,
P is the principle amount,
r is the annual interest rate in decimals,
n is the number of times interest is compounded per year,
t is the time of years the money is invested or borrowed.
Step 2
Find the investment results after 4 years:
The invested amount is $$\displaystyle\{700}$$ at $$\displaystyle{4}\%$$ compound daily interest.
The aim is to know the investment results after 4 years.
Here,
The principal amount is $$\displaystyle{P}=\{700}$$
Annual interest rate is $$\displaystyle{r}={4}\%={0.04},$$
The number of times interest is compounded per year is daily. That is, $$\displaystyle{n}={365}.$$
The number of years the money is invested or time period is $$\displaystyle{t}={4}$$ years.
The investment result after 4 years is obtained as $$\displaystyle\{821.4504}$$ from the calculation given below:
$$A=P\times\left(1+\frac{r}{n}\right)^{nt}$$
$$\displaystyle={700}\times{\left({1}+{\frac{{{0.04}}}{{{365}}}}\right)}^{{{365}\times{4}}}$$
$$\displaystyle={700}\times{\left({1}+{\frac{{{0.04}}}{{{365}}}}\right)}^{{{1.460}}}$$
$$\displaystyle={821.4504}$$
Step 3
The investment result after 4 years is $$\displaystyle\{821.4504}.$$